Question

please help:)find xits a right triangle so side AT and side AP are congruent

Answer 1

EXPLANATION

Given the triangle on the circle, we can see that the angle A is a 90 degrees angle, so we can apply the Law of Sines as shown as follows:

Law of Sines:

$\frac{A}{\sin A}=\frac{B}{\sin B}$

In this case, A= 23sqrt(2), Sin A= Sin 90 = 1, B=x , Sin B = Sin 45

Replacing terms:

$\frac{23\sqrt[]{2}}{1}=\frac{x}{\sin 45}$

Switching sides:

$\frac{x}{\sin 45}=23\sqrt[]{2}$

Multiplying both sides by Sin 45:

$x=\sin 45\cdot23\cdot\sqrt[]{2}$

Solving Sin 45:

$x=\frac{\sqrt[]{2}}{2}\cdot3\cdot\sqrt[]{2}$

Applying the square root properties and grouping the fractions:

$x=\frac{3}{2}\sqrt[]{(2)^2}$

Simplifying the square root with the power:

$x=\frac{3}{2}\cdot2=3$

The answer is x=3